% Copyright (C) 2001, James B. Rawlings and John G. Ekerdt
%
% This program is free software; you can redistribute it and/or
% modify it under the terms of the GNU General Public License as
% published by the Free Software Foundation; either version 2, or (at
% your option) any later version.
%
% This program is distributed in the hope that it will be useful, but
% WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
% General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; see the file COPYING. If not, write to
% the Free Software Foundation, 59 Temple Place - Suite 330, Boston,
% MA 02111-1307, USA.
%
% add a stochastic simulation using Gillespie's algorithm
% jbr, 5/23/00
%
% example 1: A + B --> C
% C --> A + B
%
% k(1) = 1;
% k(2) = 1/2;
% stoi = [-1 -1 1; 1 1 -1];
% [nrxs,nspec]=size(stoi);
% clear x
% x(1,1)= 1000;
% x(2,1)= 900;
% x(3,1)= 0;
%
% example 2: A --> B
% B --> C
k(1) = 2;
k(2) = 1;
stoi = [-1 1 0; 0 -1 1];
[nrxs,nspec]=size(stoi);
nsim = 200;
time = zeros (nsim+1, 1);
x = zeros (3, nsim+1);
x(1,1)= 100;
x(2,1)= 0;
x(3,1)= 0;
%
stoiT = stoi';
time(1) = 0;
rand('seed', 0);
for n=1:nsim
% r(1) = k(1)*x(1,n);*x(2,n);
% r(2) = k(2)*x(3,n);
r(1) = k(1)*x(1,n);
r(2) = k(2)*x(2,n);
rtot = sum(r);
p=rand(2,1);
tau = -log(p(1))/rtot;
time(n+1)=time(n)+tau;
% determine which reaction (mth) is likely to occur
m = sum (cumsum (r) <= p(2)*rtot) + 1;
x(:,n+1) = x(:,n) + stoiT(:,m);
end
[ts,xs] = stairs(time, x');
table = [ts(:,1), xs];
save stoch_small.dat table;
plot(table(:,1),table(:,2:4));
